Find the zeroes of the polynomial 3-2x2-x-2-

Let f(x)=3√(2)x^2+x √(2) =(√(2)x+1)(3x √(2)) f(x)=0 , when √(2)x+1=0 or 3x √(2)=0 when x= 1√(2) or x=√(2)3 Hence the zeroes ...

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Standard VIII

Mathematics

Factorisation by Regrouping Terms

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Question

Find the zeroes of the polynomial $3 \sqrt{2} x^{2} + x - \sqrt{2}$ .

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Solution

Let $f (x) = 3 \sqrt{2} x^{2} + x - \sqrt{2}$
$= (\sqrt{2} x + 1) (3 x - \sqrt{2})$
$f (x) = 0$ , when $\sqrt{2} x + 1 = 0$ or $3 x - \sqrt{2} = 0$
when $x = - \frac{1}{\sqrt{2}}$ or $x = \frac{\sqrt{2}}{3}$
Hence the zeroes of the polynomial
$3 \sqrt{2} x^{2} + x - \sqrt{2}$ are $- \frac{1}{\sqrt{2}}, \frac{\sqrt{2}}{3}$

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Find the zeroes of the polynomial 3√2x2+x−√2.

Let f(x)=3√2x2+x−√2=(√2x+1)(3x−√2)f(x)=0, when √2x+1=0 or 3x−√2=0when x=−1√2 or x=√23Hence the zeroes of the polynomial3√2x2+x−√2 are −1√2,√23

Find the zeroes of the polynomial $3 \sqrt{2} x^{2} + x - \sqrt{2}$ .